Introduction
Aerosol–cloud interactions remain the largest source of uncertainty in
projections of anthropogenic climate change, and aerosol–ice interactions, in
particular, are poorly understood (). Atmospheric aerosol
may modulate the properties of pure ice clouds by providing particles upon
which new ice crystals form. Cirrus clouds control moisture transfer into the
lower stratosphere and can have a net warming effect (e.g., ).
Ice crystals within cirrus clouds can be formed in a variety of ways.
Heterogeneous nucleation refers to the formation of ice on an aerosol
surface, and the portion of aerosol upon which ice forms this way are called
ice-nucleating particles (INP). There are several modes of heterogeneous
freezing: in deposition nucleation, vapor deposits directly onto an aerosol;
in condensation freezing, the aerosol acts first as a cloud condensation
nucleus and then immediately as an INP; and in immersion freezing, an aerosol
submerged for some time in supercooled liquid eventually initiates ice
formation. Ice crystals may also form directly from an aqueous phase through
homogeneous nucleation, typically at temperatures below about 235 K
(). Aircraft measurements of relative humidity and ice crystal
number concentrations indicate that heterogeneous nucleation is dominant for
synoptic cirrus over North and Central America (). But both
mechanisms can be active in cirrus clouds, and the competition for water
vapor between homogeneous and heterogeneous ice nucleation must be included
in cirrus formation parameterizations ().
Much effort has been devoted to studying heterogeneous ice nucleation on a
fundamental level (e.g., ). Ice nucleation
can be understood as the formation of an ice germ in the vicinity of an
active site. The nature of active sites is unknown, but current understanding
suggests that they promote ordering of the water molecule layers near the
particle surface. The active site density refers to the number of these sites
per unit of aerosol surface area. A particle with more surface area will tend
to have more active sites and nucleate at higher temperatures (or lower
supersaturations); however, each active site varies in its efficiency, so
that contact angle or site density distributions are necessary
().
While Köhler theory is the accepted framework to describe droplet
activation, nothing analogous exists for ice. Two conceptual paradigms are
currently in use: stochastic and singular freezing ().
In the stochastic paradigm, water molecules fluctuate randomly to and from a
particle surface with some probability of reaching a critical, stable germ
size that initiates formation of the new phase; homogeneous nucleation within
a supercooled droplet is understood this way. In the singular paradigm,
nucleation is determined solely by particle surface morphology; once a
characteristic threshold temperature or supersaturation is acquired, ice
nucleates.
Parameterizations of heterogeneous ice nucleation calculate the
heterogeneously formed ice crystal number, Ni,het, as a function of
thermodynamic conditions and precursor aerosol properties. These
parameterizations, termed INP spectra hereafter, may be empirically or
theoretically based. Empirical spectra use lab or field data to calculate an
active site density. Theoretically based spectra use classical nucleation
theory (CNT) and calculate a nucleation rate proportional to the aerosol surface
area (e.g., ). The surface
heterogeneity should also be considered and has recently been represented as
a distribution of contact angles (). But ice
nucleation data is geographically or thermodynamically limited, taken only
in localized regions or over a narrow range of temperatures and pressures.
And classical nucleation theory is approximate and requires unknown or
variable surface property data. As a result, the output of INP spectra has
remained uncertain, with up to 3 orders of magnitude difference in
calculated Ni (e.g., ).
Early published INP spectra expressed active site density as a function of
only temperature or supersaturation and neglected the aerosol composition and
size. For example, Fletcher 1969 proposed a parameterization based solely on
temperature, valid down to about -25 ∘C. The INP
spectrum describes deposition and condensation nucleation as a function of
supersaturation only, with data from a continuous-flow diffusion chamber.
They observed a logarithmic increase in the number of ice-nucleating aerosol
with supersaturation with respect to ice, si.
More recently published INP spectra consider the effects of size distribution
and composition of ice-nucleating particles. For example,
(PDA08) calculates the active site density for mineral dust, black carbon
and hydrophobic organics, constrained with data from the First and Second Ice
Nuclei Spectroscopy Studies (INSPECT-1 and -2) and the Cirrus Regional Study
of Tropical Anvils and Cirrus Layers – Florida-Area Cirrus Experiment
(CRYSTAL-FACE) (). Updates have been made in the
spectrum (; PDA13). PDA08 and PDA13 are
based on the singular paradigm, in which each aerosol type nucleates ice at
threshold temperatures and supersaturations. Several other studies have
parameterized nucleation efficiency of mineral dusts or illite powders, using
cloud chamber data or optical microscopy (e.g.,
).
have also developed an INP spectrum at
cirrus-relevant temperatures, using the Aerosol Interaction and Dynamics in
the Atmosphere (AIDA) cloud chamber data for hematite particles
(). This study uses the three aforementioned spectra to
describe deposition nucleation. Other empirical spectra and recent
heterogeneous ice nucleation experiments are further discussed in the review
by .
Numerous studies have examined the impact of INP spectrum on nucleated ice
crystal number. Using the NCAR Community Atmosphere Model (CAM),
evaluated how predicted cloud type, cloud properties and
radiative balance change based on the INP spectrum (). The
study uses as a default spectrum compared to ,
a spectrum which links Ni with the aerosol number of diameter
larger than 0.5 µm. The DeMott spectrum
calculated a much lower Ni, and hence a higher liquid water path
and lower ice water path for Arctic mixed-phase clouds. Curry and
Khvorostyanov have also run , , , and their own theoretical
INP spectra with parcel model simulations over a range of thermodynamic
conditions (). The authors emphasize the importance of
applying empirical spectra only in their regions of validity and note that
low nucleating efficiencies in PDA08 may underestimate ice crystal number.
noted that significantly overpredicted
ice water content in coupled models if aerosol were not depleted after
nucleation (). When INP depletion was included, the
predictions of water and ice in mixed-phase clouds improved considerably.
compared the output crystal number between PDA08,
, and the CNT spectrum
for both monodisperse and polydisperse aerosol (). They
found that ice nucleation occurred more often in the competitive regime for
the spectrum, yielding smaller crystal numbers; however, PDA08
predicted higher crystal numbers with ice nucleation most frequently in the
homogeneous regime. Similar results have also been reported for mixed-phase
cloud conditions (e.g., ).
In this work, we extend the adjoint of a cirrus formation parameterization
() to perform sensitivity analysis for several
heterogeneous INP spectra. Adjoints can calculate the sensitivity of a given
output to all inputs more efficiently and accurately than finite difference
runs, but at the expense of code development ().
have constructed the adjoint model of a liquid droplet
parameterization, and others have used adjoints for data assimilation, for
example in the Community Multiscale Air Quality and ISORROPIA models
(). Here we use the adjoint approach to
address the following: how and why Ni and its sensitivities change
with the INP spectrum used and how sensitivities can elucidate nucleation
regime and efficiency. Our focus is on spatial and temporal output
variability, distinct from output uncertainty. The development of
heterogeneous ice nucleation spectra reduces parameter uncertainty; once a
spectrum is chosen, the question of how input variables contribute to output
variability remains. We consider the latter here. Section
provides an overview of the nucleation parameterization, model inputs and
four INP spectra used. Crystal number fields and aerosol acting as INP are
presented in Sect. and .
Sensitivities of different spectra are discussed in
Sect. to , and
Sect. summarizes the work.
Methods
BN parameterization
We use the Barahona and Nenes cirrus formation parameterization (BN09)
() and its adjoint (). BN09
describes the competition for water vapor between heterogeneous and
homogeneous nucleation; the number of heterogeneously formed crystals,
Ni,het, is calculated from any of a variety of nucleation spectra,
and homogeneously formed number, Ni,hom, is calculated with an
approximate solution to the coupled mass and energy balances of a cirrus
cloud parcel. Then the total ice crystal number, Ni, is the sum of
the heterogeneous and homogeneous contributions (Eq. ). When
the temperature is greater than about -38 ∘C, homogeneous
nucleation ceases because it is kinetically unfavorable. Homogeneous
nucleation is also suppressed when the number of INP exceeds a certain
threshold, Nlim, and the maximum supersaturation that develops
within the cloud parcel, smax, is less than the threshold for
homogeneous nucleation, shom. In this case, smax must be
numerically calculated from the growth and supersaturation evolution
equations.
Ni=Ni,hom+Ni,het(shom),Ni,het(shom)<NlimNi,het(smax),Ni,het(shom)≥Nlim
The BN parameterization make two principal assumptions: first, ice crystal
growth occurs mostly in the free growth regime where new nucleation does not
significantly change the parcel supersaturation; second, Ni is
calculated at the maximum supersaturation rather than a supersaturation later
in the freezing pulse. These assumptions lead to overestimation of
Ni at lower temperatures and higher updraft velocities and
underestimation of Ni at lower updrafts, when the freezing pulse is
longer. For a wide range of cirrus formation conditions, however, the
parameterization output matches that of a detailed parcel model to within
5 %. These points are discussed in .
As in , the TAPENADE automatic differentiation tool was used
to create an adjoint model of BN09 (ABN15 hereafter) ().
For the finite series of operations that link Ni to the inputs in
BN09, TAPENADE uses the chain rule to propagate a perturbation in the output,
dNi, back to differentials in the input variables. Once
developed, the adjoint model saves significant computational time, relative
to a finite difference method, and avoids both approximation and truncation
errors. ABN15 differentiates Ni with respect to 13 input variables:
temperature; updraft velocity; accumulation- and coarse-mode dust numbers and
diameters; organic aerosol number and diameter; black carbon number and
diameter; sulfate number and diameter; and water vapor deposition
coefficient. All derivatives, along with the typical output of BN09, are
evaluated at the input model state for each grid cell and time step of a
GCM (global climate model) run. ABN15 is verified with centered finite difference approximations, using
perturbations of ±0.1 % around each input for simulation-relevant
thermodynamic and aerosol conditions. Such finite difference calculations
require two runs for each variable, so for 13 input variables, the adjoint
model saves 25 executions of the parameterization relative to typical
sensitivity calculations.
Simulation setup and spectra
Simulation inputs are generated from the NCAR Community Atmosphere Model,
version 5 (CAM5) at the 232 hPa pressure level with 2-year spin-up and
2.5 × 1.88∘ resolution. The input updraft velocity from
CAM 5.1 is calculated from the turbulent kinetic energy in the moist
turbulence scheme of Bretherton and Park 2009 as wsub=23TKE. The probability distribution of these values
is compared to 2 years' worth of millimeter cloud radar measurements (MMCR) in
Figs. S1 and S2 in the Supplement with all
values at the same latitude, longitude and altitude. Measurements are shown
after Doppler velocity decomposition, as described in .
The distribution of hourly averaged measurements has a lower maximum and
decays to smaller values than that of the hourly averaged simulation inputs.
Comparing updraft distribution from aircraft and ground-based MMCR,
note similar behavior in which the MMCR velocities were
repeatedly smaller than the in situ ones; however, saw
that lower resolution models tend to decay to even smaller values than the
MMCR observations because they do not resolve the gravity wave contribution.
This difference is probably due to the filtering of deep convective systems
within the MMCR data but no analogous filter for simulated updrafts in this
case.
We use daily averaged updraft values for which the distribution agrees better
with the observed values. wsub values from CAM are used as the
standard deviation σsub,w of a Gaussian updraft velocity
distribution P(w) of mean μsub,w=0.1 cm s-1. Both
output ice crystal numbers and sensitivities are weighted over this
distribution to account for sub-grid variability ():
f(w)‾=∫0∞f(w)P(w)dw∫0∞P(w)dw.
Adjustable parameters for ABN15 simulations.
Parameter
Value
Citation
Pressure level
232 hPa
ISCCP
Deposition coefficient
α
0.7
Width of BC SD
σBC
1.8
Width of dust SDs
σDM
1.6
Width of organic SD
σorg
1.8
Width of sulfate SD
σsulf
2.3
Liquid mixing ratio
qc
1×10-6 kgkg-1
Surface polarity
Ps
2
Organic coating
Foc
10 %
Threshold supersaturation for dust
si,0,DM
20 %
Threshold supersaturation for black
si,0,BC
35 %
Maximum nucleation efficiency of dust
eDM
50 %
Effective contact angle for dust
θDM
16∘
Maximum nucleation efficiency of black carbon
eBC
2 %
Effective contact angle for black carbon
θBC
40∘
This integration is performed numerically with a six-point Legendre–Gauss
quadrature method, with weights and abscissae chosen over an interval from
minimum to maximum velocity, which are taken as 4 standard deviations below
and above μsub,w. An upper bound of 3 m s-1, unlike that
of 0.2 m s-1 used in and , and a lower
bound of 0.001 m s-1 are enforced.
The altitude examined is in the middle of the cirrus cloud classification from the International Cloud Climatology Project (pressures between 440 and 50 hPa) and represents pure ice
cloud formation. The emissions inventory
() and MAM3 module were used (). Lognormal
size distributions are assumed for all aerosol types with geometric standard
deviations, σg, assumed to be constant and listed below in
Table . σg and total aerosol mass are used
to determine geometric mean diameter for each mode. Total aerosol number is
scaled by mass fraction to determine aerosol number concentrations in each
mode (). For calculations of ice crystal number
concentrations and sensitivities, BN09 and ABN15 were run over a year with
four heterogeneous INP spectra and daily averaged values of CAM output.
Phillips et al. (2008, 2013) empirical spectra
PDA08 uses the exponential correlation of crystal number and supersaturation
in as a reference spectrum, extending the applicable ranges of
temperature and supersaturation and incorporating characteristics of the
precursor aerosol. The number of ice-nucleating particles, nINP,X
in aerosol group X (dust and metallics – DM, black carbon – BC, or
organics – O) is calculated with a sum over the aerosol size distribution
weighted by a freezing fraction:
nINP,X=∫log0.1μm∞{1-exp[-μX(D,Si,T)]}nX(logD)dlogD.
μX represents the number of ice embryos forming per aerosol and is the
product of the active site density and aerosol surface area
():
μX=HX(Si,T)ξ(T)αXnINP,*ΩX,*πD2. nINP,* is the INP number from a reference activity
spectrum; ΩX,* is a reference aerosol surface area, which acts as a
normalization factor for the size distribution; αX is the portion of
aerosol number belonging to group X within nINP,*;
nX(logD) is the aerosol size distribution; and HX is a threshold
function that reduces INP concentrations at conditions subsaturated with
respect to water and warm sub-zero temperatures in agreement with
observations. HX equals unity at water saturation and steps at certain
threshold temperatures, T0,X, and supersaturations, si,0,X,
for the different aerosol groups. Finally ξ(T) diminishes heterogeneous
nucleation at warm sub-zero temperatures.
Both PDA08 and PDA13 adopt the mathematical framework of
Eq. (), but PDA13 employs more extensive field
campaign data (). The organic classification in PDA13 is also
split into primary biological material and glassy organics, following recent
observations of distinct ice-nucleating activity for these particle types. In
this study, sensitivity of Ni to biological INP is not considered,
as CAM5 does not currently output a biological particle number.
Classical nucleation theory spectrum
We also use the classical nucleation spectrum developed by
and presented in conjunction with the parameterization ():
nINP,X=eXnX(logD)minsisi,0,Xe-f(cosθ)khom(si,0,X-si),1,
where eX is the nucleation efficiency of aerosol group X,
si,0,X is the threshold supersaturation, nX(logD) is
the aerosol size distribution, θ is the INP-ice contact angle, and
khom is a parameter related to the homogeneous nucleation
threshold. Dust and black carbon groups are included with parameters listed
in Table ; contact angles come from the laboratory data of
and eDM is similar to that in . The
stochastic component of the nucleation efficiency through heterogeneous
nucleation rate coefficient is assumed to be negligible, and the singular paradigm
also underlies this spectrum. eX is potentially a function of temperature
and the aerosol profile, but here it is taken from literature and assumed
to be constant throughout the simulation.
(a) Nucleation regimes of cirrus in the log-log INP-ice
crystal number space. At low INP numbers, nucleation is predominantly
homogeneous. At intermediate INP numbers, nucleation is competitive between
homogeneous and heterogeneous. Beyond the threshold INP number,
Nlim, nucleation is purely heterogeneous; (b) threshold
supersaturations for homogeneous nucleation and heterogeneous nucleation on
mineral dust and BC with different organic coatings, FOC between
190 and 240 K for the PDA08 and PDA13 nucleation spectra. Both use the same
correlation for dust.
Hiranuma et al. (2014) spectrum
The nucleation efficiency of hematite particles was measured at the AIDA
chamber from -78 up to -36 ∘C and parameterized
(). The third-order polynomial fit for active site
density (in m-2) is given in Eq. () as a function
of temperature and saturation ratio of ice. Isolines from AIDA expansion
cooling experiments are interpolated over the temperature-supersaturation
space, assuming a hematite baseline surface area of 6.3×10-10 m2L-1.
ns(T,Si)=-3.777×1013-7.818×1011T+4.252×1013Si-4.598×109T2+6.952×1011T⋅Si-1.111×1013Si2-2.966×106T3+2.135×109T2⋅Si-1.729×104T⋅Si2-9.438×1011Si3
As in , we use this active site parameterization in the
framework of Eq. () to calculate nucleated crystal
number:
nINP,X=∫log0.1μm∞{1-exp[-ns(T,Si)πD2]}nX(logD)dlogD.
Hereafter, we refer to this formulation as the AIDA spectrum.
Measurement–model comparison of probability distributions in ice
crystal number concentrations. Data distributions come from the Video Ice
Particle Sampler (VIPS) and the two-dimensional stereo (2DS) probe during
April 2011 of the MACPEX campaign and the Forward-Scattering Spectrometer
(FSSP) during January 2010 of the SPARTICUS campaigns. Only measurements from
the 10–20 µm bin of the VIPS; the 5–15 µm bin of the
2DS; and the 0.89, 1.90, 3.80, 5.85, 8.30, 11.45, 14.25, 17.15 and
20.45 µm-centered bins of the 2DS are used, as approximations to
the newly nucleated ice crystal number. Measurements are also filtered for
altitudes of 232 ± 20 hPa and for uniformity, lasting at least 45 s.
Distributions of simulation output, i.e. of the annually averaged output
nucleated ice crystal number, Ni, as in Fig. ,
are shown using the (a) PDA08, (b) PDA13, (c) CNT
and (d) AIDA nucleation spectra. Different independent axes are used
in panels (c) and (d).
Results
Homogeneous and heterogeneous nucleation can be active in cirrus clouds, and
their relative influence can be conceptually understood along an
INP-Ni trace shown in Fig. a
(). When INP concentration is low, nucleation is
predominantly homogeneous. The slope or sensitivity here, ∂Ni/∂NINP, is slightly negative because the
addition of an insoluble particle slightly decreases the number of nucleated
ice crystals by competing for water vapor and decreasing supersaturation. As
the INP concentration increases, homogeneous and heterogeneous nucleation
compete more strongly for water vapor. Water vapor preferentially deposits on
the additional INP surface and depresses the number of newly nucleated
crystals, so ∂Ni/∂NINP increases in
magnitude. Eventually, INP increases beyond the threshold number,
Nlim, and further depletion of supersaturation inhibits homogeneous
nucleation altogether. Addition of another INP increases the ice crystal
number, and ∂Ni/∂NINP becomes positive.
While all nucleation for NINP<Nlim is competitive, we use
the term “competitive nucleation” below to refer to the case when both
homogeneous and heterogeneous nucleation have a significant contribution,
greater than 10 %, to Ni. These three regimes have been explained
in terms of INP number, but they can also be understood in terms of INP
diameter: increasing INP surface area leads to more vapor depletion by
heterogeneous nucleation and decreased crystal number in the competitive
regime.
This conceptual framework is used to understand the simulation results.
Crystal number
Figure shows a comparison of the in situ crystal number
measurements, taken from the NASA MACPEX (Mid-latitude Cirrus Properties
Experiment) and the DOE SPARTICUS (Small Particles In Cirrus) aircraft
campaigns. Data are used from the Video Ice Particle Sampler (VIPS) and
two-dimensional stereo (2DS) probe during April 2011 of MACPEX and from the
Forward Scattering Spectrometer Probe (FSSP) during January 2010 of
SPARTICUS. Using simultaneous Meteorological Measurement System (MMS)
pressure values, only Ni measurements taken within 20 hPa of the
simulated pressure level of 232 hPa are used. Because the newly nucleated
ice crystal number concentration is simulated, we use only Ni from
the smallest size bins of each instrument (see caption of
Fig. ). Finally, the same criterion for significant samples
as in is employed: samples must continuously span at least
45 s. These MACPEX and SPARTICUS measurements, taken with shatter-resistant
probes and analyzed with an inter-arrival time algorithm, are more reliable
than older ones, especially for the smallest size bins that we consider
().
Simulated and measured Ni agree best for the PDA13 spectrum,
followed by the PDA08 and then the AIDA spectra. The CNT spectrum
overestimates the frequencies of Ni greater than about 10 L-1
by more than 1 order of magnitude and predicts no number concentrations less
than 1 L-1. Measurements show, instead, that most of the smallest
crystals occur at lower number concentrations, below about 5 L-1. The
very high frequency of low Ni is missed by the other spectra as
well, and all except PDA13 show slower decays in the frequency of high
Ni than those in the measurements.
Model overestimate of high Ni at the coldest temperatures has been
often noted (e.g., ). Along with this
“ice nucleation puzzle” of low Ni at low temperature
(), model–measurement discrepancy may be explained by
in-cloud processes after nucleation: nucleated crystal number will tend to be
higher than in-cloud crystal number, even when looking only at the smallest
size bins. Preexisting ice crystals can inhibit ice nucleation
(), while sedimentation can significantly reduce
Ni. have termed the latter “sedimentation
induced quenching of nucleation”, and found that omission
of sedimentation by setting crystal fall speed to 0 m s-1 resulted in
higher frequency of Ni greater than 1000 L-1.
Figure a through d show the annually averaged potential
nucleated ice crystal number for each grid cell, given the vertical velocity
and aerosol profile. The spatial variability in these fields is notable and
reflects the large, documented spatial variability in INP concentrations
(e.g., ). Including additional microphysics after
nucleation will tend to reduce this spatial variability. Some common features
are still observed between fields: over the Himalayas and Rockies,
Ni is higher because orographic lifting generates stronger updrafts
and more supersaturation; the Saharan and Gobi desert outflows enhance
Ni,het; and for INP spectra considering black carbon (all except
the AIDA spectrum), higher Ni,het occurs in regions of biomass
burning (e.g., sub-Saharan Africa and the Amazon). In the Southern
Hemisphere, especially over Antarctica, heterogeneous nucleation is rare, and
Ni stays high because aerosol number concentrations are low and
active site density decreases with temperature.
Range of predicted ice-nucleating particle numbers and abundances
for different nucleation spectra.
Spectrum
INP Range
Median INP
Interquartile
AINP
Median
Interquartile
[L-1]
number
range of INP
range
AINP
range of
[L-1]
number [L-1]
AINP
PDA08
0.047–5.07
0.48
1.05
0.0070–11.11
0.34
0.62
PDA13
0.57–28.6
3.60
10.56
0.67–49.37
10.25
10.02
CNT
6.94–1270.47
50.38
169.82
0.97–7220.64
20.80
36.52
AIDA
3.60–855.36
52.51
190.49
4.02–4549.94
20.47
24.35
Annually averaged output nucleated ice crystal number, Ni
from the cirrus formation parameterization for (a) PDA08,
(b) PDA13, (c) CNT, (d) AIDA nucleation spectra.
Elsewhere, Ni is highly variable and sensitive to the INP spectrum.
For example, all spectra except PDA08 see higher crystal number in the
Northern Hemisphere than the Southern Hemisphere. In agreement with previous studies,
PDA08 predicts the lowest INP number, between 0.047 and 5.07 L-1,
(Table ) and the highest maximum supersaturations
(). When the input aerosol number is
sufficiently high in the Northern Hemisphere, stronger competitive nucleation
results in lower Ni, while the Southern Hemisphere remains
dominated by homogeneous nucleation and higher Ni. The
heterogeneously formed fraction field in Fig. S3 also
illustrates these regions of competitive and homogeneous nucleation in the Northern Hemisphere
(NH) and the Southern Hemisphere (SH), respectively. Updraft velocity and Ni are well-correlated;
both have higher values around the equator for PDA08.
Compared to PDA08, PDA13 predicts about 1 order of magnitude higher INP
number, between 0.57 and 28.6 L-1 and more frequent inhibition of
homogeneous nucleation, as shown in Fig. S3, where the
heterogeneously formed fraction of Ni is much higher. In localized
regions of purely heterogeneous nucleation, however, PDA08 may still predict
higher Ni. This can be understood in terms of an INP abundance,
AINP≡NINP/Nlim, defined as the ratio of
available INP to the limiting number to inhibit homogeneous nucleation.
Nlim increases with decreasing maximum supersaturation,
Nlim∝Si,max/(Si,max-1), and this
increase in Nlim can outweigh the increase in INP number so that
AINP actually decreases within PDA13.
Higher Ni in PDA08 can also be understood in terms of threshold
supersaturations for nucleation, when calculated supersaturations are similar
between PDA08 and PDA13. When these thresholds are less stringent, the
competitive nucleation cusp of the INP-Ni trace becomes steeper and
extends to lower Ni values. Where nucleation is competitive, then,
as in PDA13 around the equator, very low Ni is possible.
Compared to PDA13, INP numbers in the CNT and AIDA spectra are about 10-fold
higher, with median values of 50.38 and 52.51 L-1, respectively.
High INP numbers result in almost purely heterogeneous nucleation everywhere
for the CNT spectrum, as shown in Fig. S3c. The highest crystal
numbers in any of the fields occur for this spectrum in Saharan outflows
because of the high dust nucleation efficiency and the dependence on aerosol
number concentration rather than surface area here. Large accumulation-mode
dust numbers can yield large AINP. Ni is on the order
of 1000 L-1 here, larger than any of the in situ measurements
shown in Fig. . An overestimate of INP by CNT-based spectra
has been reported elsewhere (e.g., ).
Annually averaged contributions of dust and BC to
heterogeneously formed ice crystal number. (a) Dust contribution in
PDA08; (b) dust contribution in PDA13; (c) black carbon
contribution in PDA08; and (d) black carbon contribution in PDA13.
For the AIDA spectrum, mostly heterogeneous nucleation occurs in the Northern
Hemisphere, while competitive nucleation occurs in the Southern Hemisphere.
INP increases lead to frequent inhibition of homogeneous ice nucleation for
these last two spectra. Again, higher Ni are due to higher
AINP; here, the increase in Nlim with decreasing
supersaturation is not enough to outweigh the higher INP numbers.
A final point can be made about the strong temperature dependence of the
threshold supersaturation for homogeneous nucleation. Within the CNT
spectrum, the heterogeneously formed fraction of Ni actually
increases in the SH (Fig. S3) because at the coldest
temperatures, the threshold supersaturation for homogeneous nucleation
significantly increases, as shown in Fig. b. A
fewer number of INP are needed to depress the supersaturation enough to
inhibit homogeneous nucleation; the dust INP in the CNT simulations are
efficient enough to shut down homogeneous nucleation.
Nucleating aerosol
We consider next which aerosol groups act as INP in the regions of purely
heterogeneous nucleation. For PDA08 in Fig. a and c,
both dust and black carbon play a role. Gradients in input temperature and BC
contribution both appear around 40∘ S because the BC threshold
supersaturation is a quadratic function of temperature in this spectrum
(Fig. b) (). Below
60∘ S, the BC contribution is 40 % or higher for PDA08. This is
unexpected because black carbon sources tend to be continental and
anthropogenic, while land coverage and population density are lower in the
SH.
For PDA13, dust is by far the primary contributor to Ni,het outside
of a very localized region of deep convection around the Equator. The
correlation for si,0,DM remains the same between PDA08 and
PDA13 and decreases with decreasing temperature because observations show
that nucleation on dust generally becomes more efficient at colder
temperatures (e.g., ). PDA13 also uses an updated
correlation for Si,0,BC, expressed in terms of surface
polarity and organic coating:
Si,0BC=S̃i,0+δ01(FOC,FOC,0,FOC,1)×[1.2×Siw(T)-S̃i,0],
where S̃i,0 is a baseline supersaturation of 30 %, δ01
is a cubic interpolation over organic coating, FOC, between lower
and upper bounds of FOC,0 and FOC,1
(), and Siw is the saturation
ratio of vapor with respect to ice at exact water saturation, since minimal
nucleation has been observed at water-subsaturated conditions for
heavily coated black carbon (). Surface polarity expresses
hydrophilicity and is operationally defined as the number of water monolayers
adsorbed to the aerosol surface at 50 % relative humidity, while the
organic coating indicates the fraction of BC surface covered in insoluble
organics. These parameters are source-dependent and difficult to determine,
but this study assumes a high surface polarity of two monolayers and a low
organic coating of 10 % to maximize any impact of black carbon
(Table ). have also shown that these
values describe aircraft engine combustion emissions, which would be relevant
at this altitude.
The different aerosol contributing to INP concentrations, despite the same
framework, can be understood by analyzing the expression for μX. Given
that the same aerosol size and number distributions have been used in both
runs (Table ), the difference is in the active site
density parameterization. The observationally based terms making up the
active site density are a threshold for water-subsaturated conditions, a
threshold for warm sub-zero temperatures, a background aerosol number, and a
baseline surface area mixing ratio ():
nS,X=HX(Si,T)ξ(T)αXnINP,*ΩX,*.
Between PDA08 and PDA13, the portion of aerosol belonging to the BC group,
αBC, has increased by 3 %, while our input temperatures are
too low for the warm sub-zero temperature threshold, ξ(T), to affect
NINP calculations. The water-subsaturated threshold, HX, would
completely suppress BC nucleation if FOC were taken to be 100 %;
experimental evidence has shown that BC nucleation may only occur at water
saturation when coating is significant (). But we have
used FOC of 10 % and the threshold supersaturation has actually
decreased for PDA13, as shown in Fig. b. These
factors alone actually yield a higher active site density for BC than for
dust.
The difference in contributions, then, is the result of changing baseline
surface area mixing ratios, ΩX,*. A lower active site density is
needed to obtain the same freezing fraction when ΩX,* is higher.
Between PDA08 and PDA13, this parameter decreases 4-fold from 2×10-6 to 5×10-7 m2kg-1 for dust and increases
about 3-fold from 1×10-7 to 2.7×10-7 m2kg-1 for BC. As a result, the freezing fraction of
BC is much lower, even if nS,BC is somewhat higher. Dust becomes
the primary INP for PDA13 because its freezing fraction has increased.
Ni from PDA13 is lower in the NH because the large dust numbers
there depress Ni,hom, as shown in Figs. and
S3.
Annually averaged accumulation-mode dust number sensitivities for
(a) PDA08, (b) PDA13, (c) CNT and
(d) AIDA.
Surface polarity and organic coating parameters are prescribed in these
simulations and may be highly variable in the atmosphere. We have chosen a
high polarity and low organic coating, so that BC contribution calculations
represent an upper bound. For simulations with higher organic coatings, any
INP contribution from BC disappears completely. But polarity and coating
change with morphology and porosity, which change with source
(). A more detailed consideration of the BC emissions
inventory would be needed to more accurately determine these parameters and
BC contribution to crystal number. Uncertainty also exists within the BC
emissions inventory itself, and this, along with the coating and polarity
parameters, will translate to uncertainty in the Ni field.
Nucleation regime
The sign and magnitude of the insoluble aerosol number sensitivities,
∂Ni/∂NINP, can be used to elucidate the
active nucleation regime. Figure gives an example with
the annually averaged sensitivity of Ni to accumulation-mode dust
number, ∂Ni/∂Ndust,a, for all spectra. In
the Southern Hemisphere, sensitivities for PDA08 are of small magnitude
(O(10-4)) and negative, as homogeneous nucleation dominates.
There are localized regions of strong competitive nucleation in sub-Saharan
Africa and northern South America, where sensitivities are of larger
magnitude (O(10-3)) and negative. Sensitivities throughout
most of the Northern Hemisphere are of moderate magnitude and negative,
indicating weaker competitive nucleation.
The CNT field exhibits positive sensitivities throughout most of the Northern
Hemisphere, delineated in white and indicating purely heterogeneous
nucleation. PDA13 also contains regions of purely heterogeneous nucleation
but around the Equator in regions of lower updraft and higher INP. When
updraft velocity increases significantly – in the region of deep convection
over Indonesia or over the Himalayas or Rockies due to orographic lifting –
a sufficiently high supersaturation may be generated to exceed the threshold
for homogeneous nucleation and induce competitive nucleation. For both the
PDA13 and AIDA spectra, regions of large and negative sensitivities, or
strong competitive nucleation, appear south of 60∘ S. INP numbers
are considerably lower than Nlim here, but the threshold
supersaturation for homogeneous nucleation has also increased at these cold
temperatures.
Time series of accumulation-mode dust number sensitivities (green,
in LL-1) and input updraft velocities (blue, in ms-1)
over Indonesia at 2.9∘ S, 135∘ E for (a) PDA08 and
(b) PDA13; and over South America at 0.95∘ N ,
64∘ W for (c) PDA08 and (d) PDA13.
The magnitude of negative sensitivities during competitive nucleation reflect
the threshold conditions assigned to a given aerosol group. The lower the
threshold supersaturation for an aerosol group, the more readily it nucleates
and the more effectively it depletes water vapor; this corresponds to larger
magnitude ∂Ni/∂Ndust,a before
NINP surpasses Nlim and purely heterogeneous nucleation
begins. PDA13 sensitivities to BC number are of larger magnitude than PDA08
values because Si,0,BC is lower for the polarity and
FOC values used here. The cusp of the INP-Ni trace
becomes steeper, and the competition for water vapor is stronger in this
case.
∂Ni/∂Ndust,a is of large magnitude
(O(10-2)) and positive for the AIDA spectrum due to larger
predicted INP numbers. These sensitivities decrease in magnitude over the
Antarctic because the active site density parameterization has a strong
supersaturation dependence at cold temperatures (Fig. S5). If the
temperature decreases by 5 K for a constant supersaturation, the active site
density can drop by as much as 25 %. The effect of this active site density
parameterization on Ni is discussed further in
Sect. . ∂Ni/∂Ndust,a
also decreases in magnitude over Indonesia because the large updrafts here
generate enough supersaturation that competitive nucleation occurs often and
reduces the annually averaged magnitude of ∂Ni/∂NINP.
Along with these spatial sensitivity patterns, we look at sensitivity time
series without temporal averaging, which show the frequency of occurrence of
different nucleation regimes. Infrequent but large magnitude sensitivities
can have an important influence on the annual average ().
Distributions of both accumulation-mode dust number sensitivities and input
updraft velocities are presented at (2.9∘ S, 135∘ E) over
Indonesia and (0.95∘ N, 64∘ W) over northern South America
in Fig. . These points are denoted by diamonds in
Fig. . Their annually averaged sensitivities differ
significantly, despite their being in the same latitudinal band with similar
aerosol loadings.
The location over Indonesia experiences high updraft more frequently, and the
additional supersaturation generation translates to more competitive
nucleation and larger magnitude sensitivities in PDA13, almost down to
-0.1 LL-1. In PDA08, more supersaturation generation
translates to more frequent homogeneous nucleation and smaller magnitude,
less variable sensitivities, on the order of 10-3 L L-1. The
location over South America has fewer instances of high updraft, so for
PDA13, the system cannot always overcome the threshold supersaturation for
homogeneous nucleation. Purely heterogeneous nucleation occurs more
frequently: Fig. d has primarily positive
sensitivities of small magnitude with an occasional large spike in ∂Ni/∂Ndust,a, which always corresponds to a large
updraft. Relative to PDA13, PDA08 exhibits stronger water vapor competition:
the peaks in Fig. c are about 4 times as large as
those in Fig. a. This behavior can be understood in
terms of a transition along the INP-Ni trace in
Fig. a: Ni and ∂Ni/∂NINP respond differently to supersaturation
generation based on how many INP the nucleation spectrum predicts.
Log-space distributions of a random sampling of
(a) accumulation- and coarse-mode dust number and (b) dust
diameter for PDA08, PDA13 and AIDA spectra during purely heterogeneous
nucleation. The box is constructed with 25th percentile, q1; median,
q2; and 75th percentile, q3. Outlying points are marked with crosses if
they fall outside [q1-1.5(q3-q1),q3+1.5(q3-q1)].
INP nucleation efficiency
The positive values of ∂Ni/∂NINP, for which
nucleation is purely heterogeneous, can be understood as nucleation
efficiencies: those aerosol which act as efficient INP generate a large
increase in crystal number for a given increase in aerosol number. Rather
than an inherent nucleation efficiency of a certain aerosol group, the
sensitivity reflects an INP efficiency given the particular model state.
Accumulation-mode dust has a mean efficiency of 0.0012 %
(O(10-3 %)) in PDA08 and 0.079 % (O(0.1 %))
in PDA13, while coarse-mode dust has a mean efficiency of 0.61 % in PDA08
and 0.078 % in PDA13. AIDA calculates considerably higher mean efficiency
of 1.4 % for the accumulation mode and 52 % for the coarse mode. Black
carbon in PDA08 is 0.03 % efficient on average, 1 order of magnitude
higher than the accumulation-mode dust. In PDA13, on the other hand, black
carbon efficiency is an order lower than accumulation-mode dust and skewed
toward lower values (not shown). Efficiency of organic aerosol is negligible,
on the order of 10-5 % and skewed to values as low as 10-12 %.
From Eq. () during purely heterogeneous nucleation,
∂Ni∂nX=1-exp(-ns(Si,T)πD2).
As the number of embryos per aerosol particle becomes large, the
nucleation-active fraction of the aerosol population, which is equivalent to
the positive aerosol number sensitivity or the nucleation efficiency,
approaches unity. This occurs because the product of active site density and
aerosol surface area becomes large enough that an ice embryo should always
form on the INP surface. Shifts in the number sensitivities reflect changing
contributions to Ni,het. To illustrate, Fig. a shows
the distribution of a random sample of 5000 daily averaged dust number
sensitivities, when ice nucleation is purely heterogeneous, i.e. ∂Ni/∂NINP>0. The coarse-mode dust number sensitivity
is higher, and the accumulation-mode dust sensitivity is lower for PDA08 than
PDA13 because BC nucleation has been suppressed in the latter. The active
site density of PDA08 BC is larger than that of dust under certain conditions
(Fig. S5), meaning that BC efficiencies are higher than the
accumulation-mode dust efficiencies because aerosol diameter for the two
groups is assumed to be the same. The coarse-mode sensitivities or
efficiencies are even higher because their surface area is 2 orders of
magnitude larger and outweighs a lower active site density.
The PDA08 distributions also have many more outliers because of the greater
competition for water vapor between aerosol groups. The adjoint sensitivities
are local in space and time, and in model grid cells without BC, dust in both
modes is able to nucleate much more efficiently. In grid cells with more BC,
the dust nucleation efficiency is significantly reduced because of the
competition for water vapor between the two INP groups. The narrower range of
AIDA efficiencies reinforces this point: this spectrum describes nucleation
by dust in idealized conditions, and no other aerosols compete for water vapor.
Its active site parameterization also contains no threshold functions that
abruptly reduce nucleation. For application in global models, it may be more
effective to use parameterizations from experiments with multiple nucleating
aerosol types.
Once an aerosol population has reached its maximum active fraction or
efficiency, Ni becomes less sensitive to the number of these
aerosol. In PDA13, the coarse-mode dust population reaches an upper bound in
its efficiency, and Ni sensitivity to coarse-mode number decreases
to a value comparable to the accumulation-mode number. For low active
fractions, Eq. () can be linearized so that
fIN∼O(ns(Si,T)D2). Given that
ns∼O(109 m-2) and D∼O(10-6 m) in
the coarse mode (Fig. S5), the maximum active fraction is expected
to be on the order of 10-3, which is indeed the value seen in
Fig. .
Size sensitivity and the active site density
Diameter sensitivities can also be understood in terms of nucleation regime.
When nucleation is purely heterogeneous, diameter sensitivity is positive;
increasing aerosol diameter increases crystal number because for a given
active site density, more surface area increases the number of ice embryos
per aerosol. During competitive nucleation, diameter sensitivity becomes
negative, as more available surface area for heterogeneous nucleation reduces
Ni from Ni,hom. As with number sensitivity, the magnitude
of negative diameter sensitivities reflects how intensely a certain aerosol
group can deplete water vapor. The magnitude of positive diameter
sensitivities is larger for coarse mode than accumulation-mode dust in all
spectra (Fig. ); an incremental increase in diameter generates
more surface area for larger particles than for smaller particles.
The magnitude of positive diameter sensitivities also reflect active site
density. From Eq. (), during purely heterogeneous
nucleation,
∂Ni∂D=2πDnXns(Si,T)exp(-ns(Si,T)πD2)
which shows that ∂Ni/∂D∝Dexp(-D2)
and ∂Ni/∂D∝nsexp(-ns). The
magnitude of diameter sensitivity first increases, then decreases, with
diameter. The larger the diameter, the faster the sensitivity decreases after
its maximum and the larger that maximum sensitivity. Again for active site
density, the magnitude of diameter sensitivity first increases then decreases
with ns. And the larger the active site density, the faster the
sensitivity decreases after reaching its maximum value. The first effect is
stronger because ∂Ni/∂D is proportional to active
site density but to the square of diameter.
Figure b is constructed again from a random sample of 5000
daily averaged dust diameter sensitivities in the purely heterogeneous
regime, i.e. ∂Ni/∂DINP>0. The maximum
coarse-mode diameter sensitivity is smaller than that of the accumulation-mode diameter sensitivity for PDA13 and CNT because the higher number of
accumulation-mode dust particles outweighs the larger coarse-mode surface
area. The AIDA and PDA13 spectra tend to reach the same maximum diameter
sensitivities (10-11 µm cm-3 in the coarse mode) as both
have reached their maximum active fraction. These features do not
characterize the PDA08 distributions because of competition for water vapor
with black carbon. Given the higher active site density and equal surface
area of black carbon relative to accumulation-mode dust, ∂Ni/∂Ddust,a is smaller than in the other spectra.
The surface area increase from the addition of a coarse-mode dust particle
outweighs the higher BC active site density and ∂Ni/∂Ddust,c in PDA08 is comparable to the values in the other spectra.
In summary, spectra with large active site densities will be highly sensitive
to aerosol diameter over a limited range of these diameters, while spectra
with lower active site densities will be less sensitive to aerosol diameter
but over a larger range of these diameters. These trends may be convoluted by
competition for water vapor with other aerosol species.
Sensitivity of Ni to temperature and sulfate aerosol
The above discussion has focused on insoluble aerosol sensitivities. Soluble
aerosol sensitivities, ∂Ni/∂Nsulf, are
always positive because the addition of these soluble particles enhances
homogeneous nucleation and crystal number, regardless of the insoluble INP
profile. When purely heterogeneous nucleation occurs, ∂Ni/∂Nsulf is zero. Sulfate sensitivities are
generally on the order of 0.001 cm3cm-3 but can be as large
as 0.025 cm3cm-3 at the coldest temperatures in the SH. This
field does not change in magnitude between spectra because the treatment of
homogeneous nucleation is identical in all cases. ∂Ni/∂Nsulf is smaller and less influential than the
updraft sensitivity fields, similar to the findings of , for
which the aerosol size distribution did not strongly affect the number of
nucleated ice crystals.
Temperature sensitivities, ∂Ni/∂T, are generally
negative because colder temperatures tend to facilitate ice nucleation. An
increase in temperature may exceed the threshold temperature for a certain
aerosol group, deactivating it, and allowing homogeneous nucleation to
generate a larger Ni. This phenomenon can be observed in both the
PDA08 and PDA13 fields, in which positive sensitivities fall exclusively at
the outflow of Saharan dust around the equator where input temperature is
between 225 and 230 K. These temperatures are in the range at which
the water-subsaturated threshold function for dust drops (T0DM=-40 ∘C and ΔT=5 ∘C), so that the primary
contributor to heterogeneous nucleation depletes less water vapor and
homogeneous nucleation yields higher Ni.
The magnitude of ∂Ni/∂T is smaller than expected
from classical nucleation theory, probably due to counterbalancing effects.
For example, as temperature increases so does water vapor diffusivity, which
enhances crystal growth and reduces crystal number. But latent heat of sublimation
also increases as temperature drops, which slows the crystal growth rate. The
homogeneous nucleation coefficient increases by 1 order of magnitude with
only a 30 K drop in temperature (). The threshold
supersaturation for dust, however, also goes down, so that deposition
nucleation can more easily inhibit homogeneous nucleation. These various
temperature dependencies may cancel out and lead to lower temperature
sensitivities within the model. have noted an intermediate
regime in nucleation experiments for which ns isolines are independent of
temperature and change primarily with supersaturation. Similar compensating
effects, which cause low temperature sensitivity in the parameterization
runs, might also explain this experimentally observed,
temperature-independent regime.
Summary
Thorough understanding of nucleated ice crystal variability in global
simulations will help improve model representation of cirrus clouds and their
radiative forcing. Towards this end, adjoint sensitivity analysis provides a
powerful and efficient means of quantifying the prevalent ice nucleation
regime, active site density and inputs driving temporal and spatial
variability in the model output. From analysis of a single GCM simulation for
each nucleation spectrum, using CAM 5.1 and current day emissions, we have
shown the following results:
Nucleation regime is determined by INP, but Ni is determined by threshold conditions and INP abundance.
During a simulation, the number of ice-nucleating particles predicted by a
nucleation spectrum determines its nucleation regime, or equivalently where
the system “sits” along the INP-Ni trace. Threshold
supersaturation and the number of INP relative to the limiting number
determine the nucleated ice crystal number. Lower ice crystal numbers can be
calculated in spite of higher INP, if certain aerosols have less stringent
threshold supersaturations, because si,0,X affects the steepness
and depth of the competitive cusp on the INP-Ni trace. At the
coldest temperatures, strong supersaturation dependence of active site
parameterizations may also reduce Ni. In addition, the number of
INP only dictates ice crystal number relative to the limiting number to
prevent homogeneous nucleation in this framework. If Nlim
calculated in one spectrum is lower relative to another, this spectrum may
still calculate higher crystal number with fewer ice-nucleating particles.
The baseline surface area mixing ratio, ΩX,*, strongly affects which INP contribute to
Ni. The suppression of certain INP groups manifests as a shift in the aerosol number sensitivity distributions. Dust contribution to
heterogeneously formed number dominates on a global scale for PDA13 runs.
Deconstructing the active site density parameterization shows that this
suppression is due to a 4-fold decrease in ΩDM,* and
3-fold increase in ΩBC,*, which increases the freezing
fraction of dust significantly. Although the surface polarity and organic
coating parameters remain unconstrained, we have chosen values which would
maximize the black carbon ice-nucleating activity. The model predicts that
black carbon contribution is negligible to Ni at this pressure
level, if the PDA13 treatment is not too conservative.
Differing aerosol contributions to Ni manifest in the number
sensitivity distributions. When black carbon does not act as an INP and there
is no competition for water vapor between aerosol types, the sensitivity to
accumulation-mode dust number increases and the sensitivity to coarse-mode
dust number decreases. Glassy aerosol has a small, but regionally important
and seasonally dependent contribution in PDA13 (Fig. S4).
The sign of ice crystal number sensitivity to insoluble aerosol number or diameter indicates nucleation regime.
When insoluble aerosol number or diameter sensitivities are small and
negative, nucleation is predominantly homogeneous. When these values become
large and negative, competitive nucleation has initiated, and when the values
become positive, nucleation is purely heterogeneous. The spatial
distributions of insoluble aerosol number sensitivity, as in
Fig. , can help explain those of crystal number in
Fig. . Temporal distributions of sensitivity can also be
used to understand regime shifts along the INP-Ni trace. Spectra
that predict different INP numbers may respond differently to additional
supersaturation generation.
The magnitude of positive aerosol number sensitivity reflects heterogeneous nucleation efficiency. The sensitivity of positive diameter sensitivity reflects active site density. When nucleation is purely
heterogeneous, the magnitude of aerosol number sensitivity can be understood
as a nucleation efficiency. The range of efficiencies is limited when there
is no competition for water vapor between aerosol groups. Crystal number is
more sensitive to the aerosol species with higher associated surface areas,
until those species reach their maximum active fractions. In the same vein,
crystal number is more sensitive to the size of larger aerosol, until the
maximum active fraction is obtained. An incremental increase in the diameter
of a large particle yield greater surface area but exhausts the active site
density more quickly.
Temperature sensitivities are of smaller magnitude than expected with classical nucleation theory because of compensating temperature dependencies. Limited sensitivities to temperature reflect the empirically
observed “intermediate temperature regime”, where supersaturation is more
influential regarding nucleation.